Calculate the proceeds of $5500 due in 7 years and 8 months discounted at 4.5% 
compounded semi-annually.

To calculate the proceeds of $5,500 due in 7 years and 8 months, discounted at 4.5% compounded semi-annually, we will use the present value formula for compound interest.

The present value $ PV $ is given by:

\[
PV = \frac{FV}{(1 + \frac{r}{n})^{nt}}
\]

Where:
- $ FV $ is the future value, which is $5,500.
- $ r $ is the annual nominal interest rate, which is 4.5% or 0.045.
- $ n $ is the number of compounding periods per year, which is 2 for semi-annual compounding.
- $ t $ is the time in years.

### Step 1: Convert the time period into years
7 years and 8 months is equivalent to:

\[
t = 7 + \frac{8}{12} = 7 + \frac{2}{3} = 7.6667 \text{ years}
\]

### Step 2: Plug in the values

\[
PV = \frac{5500}{\left(1 + \frac{0.045}{2}\right)^{2 \times 7.6667}}
\]

Now, let's calculate this.

\[
PV = \frac{5500}{\left(1 + 0.0225\right)^{15.3334}} = \frac{5500}{\left(1.0225\right)^{15.3334}}
\]

Finally, we compute the present value.

\[
PV \approx \frac{5500}{(1.0225)^{15.3334}} 
\]

Let's calculate this value:The present value (or proceeds) of $5,500 due in 7 years and 8 months, discounted at 4.5% compounded semi-annually, is approximately **$3,910.14**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does changing the interest rate affect the present value?
2. What would the present value be if the amount was due in 5 years instead?
3. How is the present value different if interest is compounded annually instead of semi-annually?
4. What is the future value if the present value is $3,910.14 and it is invested for 7 years and 8 months at 4.5% compounded semi-annually?
5. How would the present value change if the time period were extended to 10 years?

**Tip:** The more frequently interest is compounded, the lower the present value, given the same nominal interest rate.

Learn how to calculate the present value (proceeds) of $5,500 due in 7 years and 8 months, discounted at 4.5% compounded semi-annually. Step-by-step solution with detailed formulas and calculations.

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